Integrate supports a variety of numerical integration techniques: - Newton-Cotes methods:
- Rectangle Rule.
- Trapezoidal Rule.
- Simpson's Rule.
- Newton's 3/8 Rule.
- Gauss-Legendre.
- Gauss-Laguerre.
- Gauss-Hermite.
- Gauss-Chebyshev First Kind.
- Gauss-Chebyshev Second Kind.
- Adaptive Simpson's method
Or, probably, dnorm is a probability distribution which includes a likeliness function, and a cumulative likeliness function, etc. I bet it doesn't work on arbitrary functions.
For what it's worth,
use integrate::adaptive_quadrature::simpson::adaptive_simpson_method;
use statrs::distribution::{Continuous, Normal};
fn dnorm(x: f64) -> f64 {
Normal::new(0.0, 1.0).unwrap().pdf(x)
}
fn main() {
let result = adaptive_simpson_method(dnorm, -100.0, 100.0, 1e-2, 1e-8);
println!("Result: {:?}", result);
}
It does seem to be a usability hazard that the function being integrated is defined as a fn, rather than a Fn, as you can't pass closures that capture variables, requiring the weird dnorm definition
https://reference.wolfram.com/language/tutorial/NIntegrateOv...
use integrate::{
gauss_quadrature::hermite::gauss_hermite_rule,
};
use statrs::distribution::{Continuous, Normal};
fn dnorm(x: f64) -> f64 {
Normal::new(0.0, 1.0).unwrap().pdf(x)* x.powi(2).exp()
}
fn main() {
let n: usize = 170;
let result = gauss_hermite_rule(dnorm, n);
println!("Result: {:?}", result);
}